MinT - Information on Result #1150508

Information on Result #1150508

Linear OOA(2¹⁴⁶, 4194305, F₂, 7, 11) (dual of [(4194305, 7), 29359989, 12]-NRT-code), using OOA stacking with additional row based on linear OOA(2¹⁴⁶, 4194306, F₂, 5, 11) (dual of [(4194306, 5), 20971384, 12]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁶, 5, F₂, 5, 5) (dual of [(5, 5), 19, 6]-NRT-code), using
  - appending kth column [i] based on linear OOA(2⁶, 5, F₂, 4, 5) (dual of [(5, 4), 14, 6]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,14P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
      - an explicitly constructive algebraic function field [i]
2. linear OOA(2¹⁴⁰, 4194301, F₂, 5, 11) (dual of [(4194301, 5), 20971365, 12]-NRT-code), using
  - OOA 2-folding [i] based on linear OOA(2¹⁴⁰, 8388602, F₂, 3, 11) (dual of [(8388602, 3), 25165666, 12]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(2¹⁴⁰, large, F₂, 3, 11), using
      - OOAs constructed from BCH codes [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.